MATEC Web of Conferences 4 4, 0 2 0 10 (2016 )
DOI: 10.1051/ m atecconf/ 2016 4 4 0 2 0 10
C Owned by the authors, published by EDP Sciences, 2016
Analysis of space payload operation modes based on divide-and-conquer
clustering
Feng Si1,2,a, Bao Jun Lin1 and Shan Cong Zhang3
1
Academy of Opto-Electronics, Chinese Academy of Sciences, Beijing, China;
University of Chinese Academy of Sciences, Beijing, China;
3
Technology and Engineering Center for Space Utilization, Chinese Academy of Sciences, Beijing, China
2
Abstract. With the development of space electronic technology, the space payload operation modes are more and
more complex, and manual interpretation is prone to errors for much workload. Generally the space payload’s
operation modes are reflected by its telemetry data. By analysing the characteristics of the payload telemetry data, it is
proposed an automatic analysis method of payload operation modes based on divide-and-conquer clustering. The
clustering method combines division and incremental clustering. The principle of the method is introduced and the
method is validated using the actual payload telemetry data. Furthermore the improved method is proposed to the
problems encountered. Experimental results show that divide-and-conquer clustering method has the feature of
calculation simple and classification accurate, when applied to the classification of payload operation modes.
Furthermore this method can be applied to the other areas of payload data processing by extending the method.
1 Introduction
The operation modes of space payload are much more
complex, as the system size becomes larger [1]. It can be
identified by the telemetry data related to the payload in
orbit. The mass telemetry data will be produced every
day and has large differences between different kinds of
payloads in general. Traditional methods either depend
on the manual judgment, or the rules according to the
prior knowledge of the designer. The rules are more
complex to design in the transient between operation
modes. Furthermore the rules designed for specific
payloads are often difficult to expand to other payloads.
In order to reduce the error rate of manual interpretation
and complexity of rule-based method, we present a novel
method based on data mining technology to find system
structure hidden in telemetry data and the operation
modes of payload automatically.
There are many kinds of technology in data mining
field [2-3]. According to the characteristics of the
payload telemetry data, we choose data clustering method
to identify the payload operation modes. Data clustering
[4-7] belongs to the category of unsupervised learning,
which is a discovery process that groups data set such
that the intracluster similarity is maximized and the
intercluster similarity is minimized. In the absence of any
prior knowledge, we don’t know the payloads how to
work and how many operation modes do they have. In
this case, the method of data clustering can help us to find
the patterns in the underlying telemetry data.
a
In this paper, we present a novel clustering algorithm
called divide-and-conquer clustering that applies group
method and incremental clustering to classify payload
telemetry data [8-11]. We demonstrate the effectiveness
of divide-and-conquer algorithm in huge actual telemetry
data of payloads. Experimental results show that this
algorithm can discover the payload operation modes
simply and effectively. Finally, we apply this algorithm
to other fields of payload data processing.
2 Divide-and-Conquer Algorithm
According to the payload’s prior work rule in orbit, much
more telemetry data was generated every day (some
greater than one hundred thousand records). There will be
great amount of calculation if we do data clustering using
one day’s records directly. In order to solve this problem,
we adapt the divide-and-conquer clustering algorithm.
Firstly, the telemetry data will be grouped in order and
then we calculate the similarity of the records in the
group, complete the clustering intra-group. Secondly,
within groups after clustering, eigenvector is calculated
for each category. Thirdly, the similarity between groups
will be calculated using eigenvectors of each category.
The process will be iterative until all records are
classified.
The process of clustering is as follows:
(1) Data pre-processing
Scan all the parameters in the data set and find out the
characteristics of each type of data parameters, such as
the parameter’s data range, discrete or continuous values,
Corresponding author: sifeng04@126.com
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits XQUHVWULFWHGXVH
distribution, and reproduction in any medium, provided the original work is properly cited.
Article available at http://www.matec-conferences.org or http://dx.doi.org/10.1051/matecconf/20164402010
MATEC Web of Conferences
or variation of the parameter. For the voltage telemetry,
temperature telemetry, or some count values of payload,
it can be applied to calculate directly. But for some state
variables, the numerical value only represents a different
state and these state variables can’t be applied for
calculation directly. These data should be pre-processed
for calculation [12-13].
(2) Normalization
All data will be normalized using the following
formula and they will be limited in the range of [0, 1]
after normalization.
xik xik min xik
1i n
max xik min xik
first group’s 100 records and their partner records with
highest similarity.
k 1, 2,..., m (1)
1i n
1i n
(3) Grouping
All the records in the data set will be grouped. In
general, the space payload operation modes are
continuous and consistent unless in fault condition. The
process of grouping can be operated in the sequence of
data in the data set.
(4) Clustering intra-group
Calculate the similarity between any two records in
the group. We’ll cluster the records according to the
similarity results. After clustering intra-group, we’ll
calculate the eigenvector of each category, which
represents the category’s centroid. The similarity between
two records can be analysed in the fractional distance
metrics [14]. The formula is as follows:
d
1/ f
distdf ( x, y ) ( xi yi ) f , f (0,1) (2)
i 1
(5) Clustering inter-group
After clustering in the groups, we’ll cluster between
groups using the selected eigenvectors of each category.
It may be grouped continually if we have many more
categories after clustering inter-group. Cluster until the
terminal conditions.
(6) Evaluation of clustering result
In order to evaluate the performance of the
classification, many other methods may be applied for
contrast, such as manual inspection of payload operation
modes, rule-based method etc.
3 Experimental Results and Discussion
3.1 The original clustering
In this section, we validate our divide-and-conquer
algorithm with an actual telemetry data set of one earth
observation payload. The data set contains several
thousand telemetry records and we choose 300 records
for test. Each record includes 206 parameters. Then we’ll
do the data set clustering in the algorithm above.
We do data pre-processing, normalization and divide
the data records into three groups and each group has 100
records. Then we calculate the similarity of records
between each other in each group. According to the
similarity result, we can find records with the highest
similarity to each record. But we can’t classify the
records only by the similarity result. Figure 1 shows the
Figure 1. The record and its partner record with highest
similarity
3.2 Analysis of clustering failure
By analysis the original records in the first group, we
have found two main reasons for clustering failure.
The first reason is disturbance of some irrelevant
parameters. Searching all parameters in the record
manually, we can find some parameters which have
drastic changes between different records. But the drastic
changes don’t reflect the system operation modes in
macroscopic view. For example, the payload heartbeat
signal, reversed once between adjacent records, reflects
only the normal state not the operation modes change.
The second reason is parameter multiplexing problem.
Some parameters are multiplexed in system design, and
each cycle represent different physical meanings.
Sometimes there is great numerical difference in different
cycle, but this difference can’t reflect the switch of
system mode.
3.3 Modified clustering method
In order to solve the above problems, we’ll take the
following measures. Firstly, we’ll apply weighted
parameters instead of original parameters in similarity
calculation. According to the characteristics of the
parameters distribution, we’ll dispatch different weights
of parameters. Secondly, we can avoid the parameter
multiplexing problem in system planning and design
phase. Alternatively we’ll use parametric subdivision for
the parameters of multiplexing in the original system
architecture. The subdivision parameters will reflect the
system operation modes.
By taking the above two measures, we re-calculate the
similarity of 100 records in the first group. The similarity
calculation results show that the similarity of the same
mode records is very high and mostly greater than 0.999.
By manual analysis of 100 records in the first group, the
group can be divided into four clusters, the 1~24 records
for the compression-and-storage mode, the 25~50 records
for the compression system power-off mode, the 51~82
records for the transmit system power-on mode, the
83~100 records for the system idle mode. The calculation
result of modified clustering algorithm is consistent with
02010-p.2
ICEICE 2016
manual analysis. Figure 2 shows the first group’s 100
records and their partner records with highest similarity.
Contrast to the result of the clustering algorithm, the
result of manual analysis is basically the same. The
following table shows the results obtained by manual
analysis.
Table 1. The Result of Manual Analysis
Clustering
Record
Operation modes
Number
Number
Figure 2. The record and its partner record with highest
similarity (using modified clustering algorithm).
Following the same algorithm, we get the other two
group records’ intra-group similarity. Figure 3 shows the
three group records’ intra-group similarity. In the figure,
we can see that the first group is divided into four clusters,
the second group has two clusters and the third group has
three clusters.
Figure 3. Clustering of every group
After completing the intra-group clustering, we’ll
calculate the centroid of each category. Using the selected
centroid of each category, we’ll calculate the similarity
between categories. The result shows that the fourth
category and fifth category can be merged into one
cluster, sixth category and seventh category can be
merged into one category. Thus the original nine
categories can be combined into seven categories. Figure
4 shows the result of second round calculation.
Figure 4. Clustering of three groups
1
1~3
Data Download from Channel 1
2
4~24
Channel 1 Close
3
25~50
Compression Stop
4
51~53
Compression Power Off
5
54~82
Transmission Close
6
83~188
Camera 1 Power Off
7
189~253
Compression and Storage
8
254~283
Idle
9
284~300
Data Download from Channel 2
When the clustering algorithm above is applied to the
rest of the data set, we can also obtain a good
classification and get the accurate payload operation
modes.
3.4 Discussion on how to divide data set
In the above chapter, we have discovered that the payload
operation modes can be automatically analysed using
divide-and-conquer clustering to the payload telemetry
data. But how to choose the best dividing method is still a
problem. We’ll discuss the best group method below.
We’ll take into account the processing time and the
clustering accuracy as the evaluation criterion. Using the
data set above, we get the result of different dividing
method. Figure 5 shows the calculation result. In the
figure, the relative processing time is calculated by the
ratio of the spending time of all dividing methods and the
un-dividing method. The clustering accuracy is got by the
ratio of successful clustering records and all the records.
Figure 5. Relative processing time and clustering
accuracy
From the figure, we can see that with the increasing
records number in each group, the processing time is
dramatically increased, but with the more clustering
accuracy. Furthermore, the increase of the processing
time is synchronous with increase of the records number
in each group. But the clustering accuracy is no longer
02010-p.3
MATEC Web of Conferences
increased when the clustering accuracy reaches a balance
point. So we can get the transition point by the balance of
the processing time and clustering accuracy. From figure
5, we can see that when the data set is divided into 3
groups and each group includes 100 records, the
clustering accuracy will reach 100% and the processing
time is only half of the un-divided method. It’s a better
choice for the payload operation modes clustering.
4 Conclusions
In this paper, we have presented a divide-and-conquer
clustering algorithm for analysing the payload operation
modes. The algorithm takes into account the group
method, weighted parameter and parametric subdivision,
which successfully solves the mass data, disturbance
parameter and parameter multiplexing problem.
Experimental results on actual telemetry data set show
that the modified algorithm can successfully identify the
payload’s operation modes automatically. The method
may be extended to the real-time processing of payload
by creating the payload characteristics library.
Furthermore when we have acquired all the operation
modes and characteristics of payload, we can do some
fault detection and fault diagnosis for the payload.
References
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
Y.F. He, G.H. Zhao, C.M. Lv, Journal of University
of Chinese Academy of Science, 28, 4(2011)
J. Han, M. Kamber, Data mining: concepts and
techniquesˈ187~198(2006)
A.K. Jain, M.N. Murty, P.J. Flynn, ACM Computing
Surveys, 31, 3(1999)
P. Hansen, B. Jaumard, Math. Program., 79, 13(1997)
A.K. Jain, R.C. Dubes, Englewood Cliffs Prentice
Hall, 32, 2(1988)
L. Kaufman, P. Rousseeuw, Finding groups in
data:An introduction to cluster analysis, 1990
C.H. Cheng, IEEE Transactions on computers, 24,
9(1975)
M.N. Murty, G. Krishna, Pattern Recognition,
12(1980)
W.F. Eddy, A. Mockus, S. Oue, Computational
Statistics & Data Analysis, 23, 1(1996)
G.A. Carpenter, S. Grossberg, Neur Netw, 3, 2(1990)
S. Asharaf, M.N. Murty, Pattern Recognition, 36,
12(2003)
H.L. Chen, K.T. Chuang, M.S. Chen, ICDM, 2005
H.L. Chen, M.S. Chen, S.C. Lin, IEEE Transaction
Knowledge and Data Engineering, 21, 5(2009)
G. Karypis, E.H. Han, V. Kumar, IEEE Computer,
32, 8(1999)
02010-p.4